Math Lab
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Heights and Distances

Trigonometry Applications · Class X

From distance d and elevation angle, compute the tower's height.

30
type a value
1100
45
type a value
189
Live values
  • Height30
  • Line-of-sight distance42.4264
  • Depression complement (deg)45
xy
  • h vs angle (for current d)

Formulas in this lab

  • Height
    h=dtan⁡θh = d\tan\theta
  • Line-of-sight distance
    d/cos⁡θd/\cos\theta
  • Depression complement (deg)
    90−θ90 - \theta
Tip: At 45 degrees of elevation, the tower's height equals the distance from your feet to its base.

Frequently asked questions

▶How do we find a tower's height?

From distance $d$ and angle of elevation $\theta$, the height is $h = d \cdot \tan\theta$. For example, standing 30 m away and looking up at 60 degrees gives $h = 30\tan 60 = 30\sqrt{3} \approx 51.96$ m.

▶How do I use this lab?

Slide the distance d and the elevation angle. The lab draws the right triangle and computes the tower height live. Try d = 50, $\theta = 45$ degrees to see h = 50 m (because tan 45 = 1).

▶Common mistake on this topic

Students mix up angles of elevation (looking up) and depression (looking down). The two are equal only when measured between the same two points. Also, drawing a clear figure with the right-angle marked saves silly errors.

▶Where do we use this in India?

Surveyors find the height of mobile towers, temple gopurams and chimneys using exactly this method. A child can estimate the height of a tall coconut tree by stepping a known distance away and measuring the angle with a simple clinometer.